Nonlinear crystalline ridge waveguides, e.g., lithium niobate-on-insulator ridge waveguides, feature high index contrast and strong optical confinement, thus dramatically enhancing nonlinear interaction and facilitating various nonlinear effects. Here, we experimentally demonstrate efficient second-harmonic generation (SHG) and cascaded fourth-harmonic generation (FHG) in a periodically poled lithium niobate (PPLN) ridge waveguide pumped with pulsed laser at the quasi-phase matching (QPM) wavelength, as well as simultaneous SHG and cascaded third-harmonic generation (THG) waves when pumped at the non-QPM wavelength. Furthermore, the ridge waveguide achieves an efficient single-pass SHG conversion efficiency of picosecond pulsed laser at ∼62%. These results may be beneficial for on-chip nonlinear frequency conversion.